Answered

Welcome to Westonci.ca, your ultimate destination for finding answers to a wide range of questions from experts. Get immediate and reliable solutions to your questions from a knowledgeable community of professionals on our platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

A machine has two components both of which have a lifespan, in months, that is exponentially distributed with mean 8. The lifespan of the two components are independent. Find the probability both components are functioning in 12 months.

Sagot :

ogorwyne

Answer:

0.0498

Step-by-step explanation:

In this question,

x~exponential

we have

mean = 1/λ = 8

from here we cross multiply, when we do

such that

λ = 1/8

probability of x functioning in 8 months

= e^-λx

= e^-1/8x12

= e^-1.5

= 0.2231

i got this value through the use of a scientific calculator

then the probability that these two are greater than 12

= 0.2231²

= 0.04977

= approximately 0.0498

therefore the probability that both components are functioning in 12 months is 0.0498

View image ogorwyne
Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.